Organ Music

The Ceremonial of Bishops, the most recent complete liturgical document from the Holy See addressing the issue, instructs that the organ remain silent during Funeral Masses, except to accompany singing.

There should be no flowers on the altar, and the music of the organ or other instruments is permitted only to assist the singing. [#824]

Hence organ preludes and postludes should not be played.

Liturgical Hints & Ideas

Liturgical music at funeral Masses is always difficult to program.
So much of the congregation may be non-Catholic or from other Catholic parishes.
Choose simple, familiar music if the congregation is expected to sing responses and hymns.
Never force people to sing; this is a difficult time for the family.
They may be able to pray better through listening than through active (and perhaps awkward) participation.
A cantor/soloist or a funeral choir can be very helpful in providing inspiring music, but should at all cost avoid sentimental selections designed to do no more than elicit tears.